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COMPOSITION OPERATORS ON UNIFORM ALGEBRAS AND THE PSEUDOHYPERBOLIC METRIC
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 Title & Authors
COMPOSITION OPERATORS ON UNIFORM ALGEBRAS AND THE PSEUDOHYPERBOLIC METRIC
Galindo, P.; Gamelin, T.W.; Lindstrom, M.;
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 Abstract
Let A be a uniform algebra, and let be a self-map of the spectrum of A that induces a composition operator , on A. It is shown that the image of under some iterate of \phi is hyperbolically bounded if and only if \phi has a finite number of attracting cycles to which the iterates of converge. On the other hand, the image of the spectrum of A under is not hyperbolically bounded if and only if there is a subspace of "almost" isometric to on which "almost" an isometry. A corollary of these characterizations is that if is weakly compact, and if the spectrum of A is connected, then has a unique fixed point, to which the iterates of converge. The corresponding theorem for compact composition operators was proved in 1980 by H. Kamowitz [17].
 Keywords
uniform algebra;composition operator;hyperbolically bounded;interpolating sequence;
 Language
English
 Cited by
1.
Interpolating sequences on uniform algebras, Topology, 2009, 48, 2-4, 111  crossref(new windwow)
2.
Fredholm composition operators on algebras of analytic functions on Banach spaces, Journal of Functional Analysis, 2010, 258, 5, 1504  crossref(new windwow)
3.
Quasicompact and Riesz endomorphisms of Banach algebras, Journal of Functional Analysis, 2005, 225, 2, 427  crossref(new windwow)
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